Chapter 28, Problem 65PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# A Van de Graaff accelerator utilizes a 50.0 MV potential difference to accelerate charged particles such as protons. (a) What is the velocity of a proton accelerated by such a potential? (b) An electron?

To determine

(a)

The velocity of proton.

Explanation

Given data:

Charge is q=1.60Ã—10âˆ’19â€‰C.

The velocity of light is c=3.00Ã—108â€‰m/s.

Potential difference is V=50.0â€‰MV.

Formula used:

The expression for Î³is,

â€ƒâ€ƒÎ³=11âˆ’v2c2v=c1âˆ’1Î³2

The relativistic kinetic energy is,

â€ƒâ€ƒKE=(Î³âˆ’1)mc2â€ƒâ€ƒâ€ƒâ€ƒ....... (1)

The kinetic energy gained by particle of charge qis,

â€ƒâ€ƒKE=qVâ€ƒâ€ƒâ€ƒâ€ƒ...... (2)

Equate the equation (1) and (2).

â€ƒâ€ƒqV=(Î³âˆ’1)mc2Î³=qVmc2+1

Substitute the given value

To determine

(b)

The velocity of electron.

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